The aim of this study was to gain knowledge of students’ beliefs and difficulties in understanding confidence intervals and to use this knowledge to develop improved teaching programs. This study took place over four consecutive teaching semesters of a one-semester tertiary statistics unit. The study was cyclical, in that the results of each semester were used to inform the instructional design for the following semester. Over the semesters the following instructional techniques were introduced: simulation with and without a computer, encouraging students to write about their work, and the use of alternative representations. As the interventions progressed, a higher proportion of students successfully defined and used confidence intervals to estimate the value of the population mean. This study also identified sources of confusion for students that can be a basis for further research.